12/11: Difference between revisions

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The (lesser) neutral second is a strangely exotic interval found between the 11th and 12th partials of the harmonic series. In Just Intonation it is represented by the [[superparticular]] ratio 12/11, and is about 150.6 [[cent|cents]] large. One step of [[8edo|8edo]] is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma (12/11)^8/2 = {{Monzo|15 8 0 0 -8}}. It follows that EDOs which are multiples of 8, such as [[16edo]] and [[24edo]], will also represent this interval well.
'''12/11''', the '''undecimal neutral second''' or '''(lesser) neutral second''', is a strangely exotic interval found between the 11th and 12th partials of the harmonic series. In Just Intonation it is represented by the [[superparticular]] ratio 12/11, and is about 150.6 [[cent]]s large. One step of [[8edo]] is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma (12/11)^8/2 = {{Monzo|15 8 0 0 -8}}. It follows that EDOs which are multiples of 8, such as [[16edo]] and [[24edo]], will also represent this interval well.


'''12/11''' differs from the larger undecimal neutral second 11/10 (~165 cents) by 121/120 (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include [[15edo]], [[22edo]], [[31edo]], [[orwell]], [[porcupine]], [[mohajira]] and [[valentine]].
'''12/11''' differs from the larger undecimal neutral second 11/10 (~165 cents) by 121/120 (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include [[15edo]], [[22edo]], [[31edo]], [[orwell]], [[porcupine]], [[mohajira]] and [[valentine]].
== See also ==
* [[11/6]] - its [[octave complement]]
* [[Gallery of just intervals]]
* [[List of superparticular intervals]]


[[Category:11-limit]]
[[Category:11-limit]]
[[Category:interval]]
[[Category:Interval]]
[[Category:just_interval]]
[[Category:Just interval]]
[[Category:neutral_2nd]]
[[Category:Neutral 2nd]]
[[Category:ratio]]
[[Category:Ratio]]
[[Category:second]]
[[Category:Second]]
[[Category:Superparticular]]

Revision as of 22:20, 31 October 2018

Interval information
Ratio 12/11
Factorization 22 × 3 × 11-1
Monzo [2 1 0 0 -1⟩
Size in cents 150.6371¢
Name undecimal neutral second
Color name 1u2, lu 2nd
FJS name [math]\displaystyle{ \text{M2}_{11} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 7.04439
Weil height (log2 max(n, d)) 7.16993
Wilson height (sopfr(nd)) 18

[sound info]
Open this interval in xen-calc

12/11, the undecimal neutral second or (lesser) neutral second, is a strangely exotic interval found between the 11th and 12th partials of the harmonic series. In Just Intonation it is represented by the superparticular ratio 12/11, and is about 150.6 cents large. One step of 8edo is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma (12/11)^8/2 = [15 8 0 0 -8⟩. It follows that EDOs which are multiples of 8, such as 16edo and 24edo, will also represent this interval well.

12/11 differs from the larger undecimal neutral second 11/10 (~165 cents) by 121/120 (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include 15edo, 22edo, 31edo, orwell, porcupine, mohajira and valentine.

See also

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